Solve for $x$ and $y$ using elimination. $\begin{align*}3x-8y &= -2 \\ 7x-7y &= 7\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-7$ and the bottom equation by $3$ $\begin{align*}-21x+56y &= 14\\ 21x-21y &= 21\end{align*}$ Add the top and bottom equations. $35y = 35$ Divide both sides by $35$ and reduce as necessary. $y = 1$ Substitute $1$ for $y$ in the top equation. $3x-8( 1) = -2$ $3x-8 = -2$ $3x = 6$ $x = 2$ The solution is $\enspace x = 2, \enspace y = 1$.